Problem: Graph this system of equations and solve. $y = 2 x - 4$ $y = \dfrac{3}{4} x + 1$ 1 2 3 4 5 6 7 8 9 10 \llap{-}2 \llap{-}3 \llap{-}4 \llap{-}5 \llap{-}6 \llap{-}7 \llap{-}8 \llap{-}9 \llap{-}10 1 2 3 4 5 6 7 8 9 10 \llap{-}2 \llap{-}3 \llap{-}4 \llap{-}5 \llap{-}6 \llap{-}7 \llap{-}8 \llap{-}9 \llap{-}10 Click and drag the points to move the lines.
Explanation: The y-intercept for the first equation is $-4$ , so the first line must pass through the point $(0, -4)$ The slope for the first equation is $2$ . Remember that the slope tells you rise over run. So in this case for every $2$ positions you move up $1$ position to the right. $2$ positions up from $(0, -4)$ is $(1, -2)$ Graph the blue line so it passes through $(0, -4)$ and $(1, -2)$ The y-intercept for the second equation is $1$ , so the second line must pass through the point $(0, 1)$ The slope for the second equation is $\dfrac{3}{4}$ . Remember that the slope tells you rise over run. So in this case for every $3$ positions you move up $4$ positions to the right. $3$ positions up from $(0, 1)$ is $(4, 4)$ Graph the green line so it passes through $(0, 1)$ and $(4, 4)$ The solution is the point where the two lines intersect. The lines intersect at $(4, 4)$.